Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with sp.spectral-theory
Search options answers only
not deleted
user 15743
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
18
votes
The first eigenvalue of the laplacian for complex projective space
The spectrum of the Laplacian of $\mathbb C P^n$ with the Fubini-Study metric is
$$Spec(\Delta_{\mathbb C P^n})=\{4k(n+k):k\in\mathbb N\} \quad\quad(*)$$
So, the first non-zero eigenvalue of $\m …
- 5,891
5
votes
Accepted
First eigenvalue of the Laplacian on Berger spheres
Tanno, the same author of the paper above mentioned in the case of 1-dim fibers, has another paper one year later [Tanno, Shûkichi. Some metrics on a $(4r+3)$-sphere and spectra.
Tsukuba J. Math. 4 (1 …
- 5,891
10
votes
Exotic spectrum of Laplace operator
Regarding the asymptotic behavior of the spectrum of the Laplacian (or, as the OP puts it, the behavior at infinity), the most basic result is Weyl's asymptotic formula (see Chavel's book, p.172): let …
- 5,891
6
votes
Lower bound on the first eigenvalue of the Laplace-Beltrami on a closed Riemannian manifold
A well-known result of Y. Colin de Verdière states that given any compact connected manifold $M$, with $\dim M\geq 3$, and any finite sequence $0<a_1\leq\dots\leq a_k$, there exists a Riemannian metri …
- 5,891
20
votes
Accepted
Avoiding integers in the spectrum of the Laplacian of a Riemann surface
I was informed by Sugata Mondal at the MPI that Scott Wolpert proved the following result in his 1994 Annals paper Disappearance of cusp forms in special families:
Theorem 5.14. The eigenvalues of …
- 5,891